Despite extensive investigations of dissipation and deformation processes in micro-and nano-sized metallic samples(1-7), the mechanisms at play during the deformation of systems with ultimate (molecular) size remain unknown. Although metallic nanojunctions, which are obtained by stretching metallic wires down to the atomic level, are typically used to explore atomic-scale contacts(5,8-11), it has not been possible until now to determine the full equilibrium and non-equilibrium rheological flow properties of matter at such scales. Here, by using an atomic-force microscope equipped with a quartz tuning fork, we combine electrical and rheological measurements on angstrom-size gold junctions to study the non-linear rheology of this model atomic system. By subjecting the junction to increasing subnanometric deformations we observe a transition from a purely elastic regime to a plastic one, and eventually to a viscous-like fluidized regime, similar to the rheology of soft yielding materials(12-14), although orders of magnitude different in length scale. The fluidized state furthermore exhibits capillary attraction, as expected for liquid capillary bridges. This shear fluidization cannot be captured by classical models of friction between atomic planes(15,16) and points to an unexpected dissipative behaviour of defect-free metallic junctions at ultimate scales. Atomic rheology is therefore a powerful tool that can be used to probe the structural reorganization of atomic contacts.